On solvmanifolds with complex commutator and constant holomorphic sectional curvature
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908412103622656 |
|---|---|
| author | Huang, Xin Zheng, Fangyang |
| author_facet | Huang, Xin Zheng, Fangyang |
| contents | An old open question in non-Kähler geometry predicts that any compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler or Chern flat. The conjecture is known to be true in dimension $2$ due to the work by Balas-Gauduchon and Apostolov-Davidov-Muskarov in the 1980s and 1990s, but is still open in dimensions $3$ or higher, except in several special cases. The difficulty in this quest for `Hermitian space forms' is largely due to the algebraic complicity or lack of symmetry for the curvature tensor of a general Hermitian metric. In this article, we confirm the conjecture for all solvmanifolds with complex commutator, extending earlier result on nilmanifolds by Li and the second named author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On solvmanifolds with complex commutator and constant holomorphic sectional curvature Huang, Xin Zheng, Fangyang Differential Geometry 53C55 An old open question in non-Kähler geometry predicts that any compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler or Chern flat. The conjecture is known to be true in dimension $2$ due to the work by Balas-Gauduchon and Apostolov-Davidov-Muskarov in the 1980s and 1990s, but is still open in dimensions $3$ or higher, except in several special cases. The difficulty in this quest for `Hermitian space forms' is largely due to the algebraic complicity or lack of symmetry for the curvature tensor of a general Hermitian metric. In this article, we confirm the conjecture for all solvmanifolds with complex commutator, extending earlier result on nilmanifolds by Li and the second named author. |
| title | On solvmanifolds with complex commutator and constant holomorphic sectional curvature |
| topic | Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2501.00810 |